The invention relates to a decoding device for code words which are protected against the occurrence of a plurality of symbol errors per code word means of a Reed-Solomon code, comprising:
a. receiving means and buffer means for the sequential storage of the code symbols of a code word; PA1 b. first arithmetic means which are connected to the receiving means in order to determine a series of syndrome symbols from the code word by means of the parity check matrix of the code; PA1 c. second arithmetic means which are fed by the first arithmetic means for solving the key equation in order to determine the positions of any incorrect symbols from the key equation by way of zero points of the error locator equation and to evaluate, using error positions thus found, associated symbol errors in order to present code symbols which are correctable by way of any position data and associated error values on a user output. PA1 d. for each code symbol said buffer means have a storage capacity for storing, together with a code symbol, an erasure indication relating to the relevant code symbol; PA1 e. a connection is provided between the buffer means and the second arithmetic means in order to correct, under the control of the erasure indication, the series of syndrome symbols as regards the effect of erasure symbols, thus forming a series of syndrome symbols which is reduced by one syndrome symbol for each erasure symbol in order to calculate any positions of error symbols therefrom; PA1 f. said second arithmetic means are suitable for treating all error symbols with erasure symbols thus localized as secondary erasure symbols; PA1 g. said second arithmetic means comprise a Galois-field arithmetic unit in order to enable, by conversion of the symbols into the associated exponent of the basic element of the Galois-field, operations to be performed on different powers of the relevant code symbol.
A device of this kind is described in the previous, non-prepublished Netherlands Patent Application No. 8302214 (PHN 10.710) corresponding to U.S. patent application Ser. Nos. 562,611 now abandoned and 824,299, in the name of Applicant which is incorporated herein by way of reference. The prior art technique concerns a code whereby a large number of errors can be repaired per code word. For this purpose complex calculations are required in order to draft the key equation, followed by solution of this equation and the error evaluator/locator expressions, inter alia by performing a so-called Chien search during which the correctness of all symbols can be successively tested when it is detected that the number of symbol errors exceeds 3. It is an object of the invention on the one hand to reduce the largest number of symbols which can be corrected per code word, thus allowing for a simplified calculation. On the other hand it is an object to perform the processing very quickly, the decoding operation then involving the direct use of any already present information concerning symbols deemed to be unreliable (so-called erasure symbols) in order to remove this pointer information from the error description and to simplify the error description. This permits using a comparatively limited amount of redundancy, correction of a number of errors which is larger than the number determined by the minimum Hamming distance for the code as a whole. This is because two redundant symbols are required per incorrect symbol when an error location is not known. When the location of an incorrect symbol is known, this error can be corrected by way of a single redundant symbol.